Millisecond exoplanet imaging: I. method and simulation results

One of the top priorities in observational astronomy is the direct imaging and characterization of extrasolar planets (exoplanets) and planetary systems. Direct images of rocky exoplanets are of particular interest in the search for life beyond the Earth, but they tend to be rather challenging targets since they are orders-of-magnitude dimmer than their host stars and are separated by small angular distances that are comparable to the classical λ/D diffraction limit, even for the coming generation of 30 m class telescopes. Current and planned efforts for ground-based direct imaging of exoplanets combine high-order adaptive optics (AO) with a stellar coronagraph observing at wavelengths ranging from the visible to the mid-IR. The primary barrier to achieving high contrast with current direct imaging methods is quasi-static speckles, caused largely by non-common path aberrations (NCPAs) in the coronagraph optical train. Recent work has demonstrated that millisecond imaging, which effectively "freezes" the atmosphere's turbulent phase screens, should allow the wavefront sensor (WFS) telemetry to be used as a probe of the optical system to measure NCPAs. Starting with a realistic model of a telescope with an AO system and a stellar coronagraph, this paper provides simulations of several closely related regression models that take advantage of millisecond telemetry from the WFS and coronagraph's science camera. The simplest regression model, called the naïve estimator, does not treat the noise and other sources of information loss in the WFS. Despite its flaws, in one of the simulations presented herein, the naïve estimator provides a useful estimate of an NCPA of ∼0.5 radian RMS (≈λ/13), with an accuracy of ∼0.06 radian RMS in 1 min of simulated sky time on a magnitude 8 star. The bias-corrected estimator generalizes the regression model to account for the noise and information loss in the WFS. A simulation of the bias-corrected estimator with 4 min of sky time included an NCPA of ∼0.05 radian RMS (≈λ/130) and an extended exoplanet scene. The joint regression of the bias-corrected estimator simultaneously achieved an NCPA estimate with an accuracy of ∼5×10^-3 radian RMS and an estimate of the exoplanet scene that was free of the self-subtraction artifacts typically associated with differential imaging. The 5σ contrast achieved by imaging of the exoplanet scene was ∼1.7×10^-4 at a distance of 3λ/D from the star and ∼2.1×10^-5 at 10λ/D. These contrast values are comparable to the very best on-sky results obtained from multi-wavelength observations that employ both angular differential imaging (ADI) and spectral differential imaging (SDI). This comparable performance is despite the fact that our simulations are quasi-monochromatic, which makes SDI impossible, nor do they have diurnal field rotation, which makes ADI impossible. The error covariance matrix of the joint regression shows substantial correlations in the exoplanet and NCPA estimation errors, indicating that exoplanet intensity and NCPA need to be estimated self-consistently to achieve high contrast.

Bayesian estimation of regularization and point spread function parameters for Wiener-Hunt deconvolution

This paper tackles the problem of image deconvolution with joint estimation of point spread function (PSF) parameters and hyperparameters. Within a Bayesian framework, the solution is inferred via a global a posteriori law for unknown parameters and object. The estimate is chosen as the posterior mean, numerically calculated by means of a Monte Carlo Markov chain algorithm. The estimates are efficiently computed in the Fourier domain, and the effectiveness of the method is shown on simulated examples. Results show precise estimates for PSF parameters and hyperparameters as well as precise image estimates including restoration of high frequencies and spatial details, within a global and coherent approach.

AIDA: an adaptive image deconvolution algorithm with application to multi-frame and three-dimensional data

We describe an adaptive image deconvolution algorithm (AIDA) for myopic deconvolution of multi-frame and three-dimensional data acquired through astronomical and microscopic imaging. AIDA is a reimplementation and extension of the MISTRAL method developed by Mugnier and co-workers and shown to yield object reconstructions with excellent edge preservation and photometric precision [J. Opt. Soc. Am. A21, 1841 (2004)]. Written in Numerical Python with calls to a robust constrained conjugate gradient method, AIDA has significantly improved run times over the original MISTRAL implementation. Included in AIDA is a scheme to automatically balance maximum-likelihood estimation and object regularization, which significantly decreases the amount of time and effort needed to generate satisfactory reconstructions. We validated AIDA using synthetic data spanning a broad range of signal-to-noise ratios and image types and demonstrated the algorithm to be effective for experimental data from adaptive optics-equipped telescope systems and wide-field microscopy.

Deblurring of breathing motion artifacts in thoracic PET images by deconvolution methods

In FDG-PET imaging of thoracic tumors, blurring due to breathing motion often significantly degrades the quality of the observed image, which then obscures the tumor boundary. We demonstrate a deblurring technique that combines patient-specific motion estimates of tissue trajectories with image deconvolution techniques, thereby partially eliminating breathing-motion induced artifacts. Two data sets were used to evaluate the methodology including mobile phantoms and clinical images. The clinical images consist of PET/CT co-registered images of patients diagnosed with lung cancer. A breathing motion model was used to locally estimate the location-dependent tissue location probability function (TLP) due to breathing. The deconvolution process is carried by an expectation-maximization (EM) iterative algorithm using the motion-based TLP. Several methods were used to improve the robustness of the deblurring process by mitigating noise amplification and compensating for motion estimate uncertainties. The mobile phantom study with controlled settings demonstrated significant reduction in underestimation error of concentration in high activity case without significant superiority between the different applied methods. In case of medium activity concentration (moderate noise levels), less improvement was reported (10%-15% reduction in underestimation error relative to 15%-20% reduction in high concentration). Residual denoising using wavelets offered the best performance for this case. In the clinical data case, the image spatial resolution was significantly improved, especially in the direction of greatest motion (cranio-caudal). The EM algorithm converged within 15 and 5 iterations in the large and small tumor cases, respectively. A compromise between a figure-of-merit and entropy minimization was suggested as a stopping criterion. Regularization techniques such as wavelets and Bayesian methods provided further refinement by suppressing noise amplification. Our initial results show that the proposed method provides a feasible framework for improving PET thoracic images, without the need for gated/4-D PET imaging, when 4-D CT is available to estimate tumor motion.

Anisoplanatic deconvolution of adaptive optics images

A modified method for maximum-likelihood deconvolution of astronomical adaptive optics images is presented. By parametrizing the anisoplanatic character of the point-spread function (PSF), a simultaneous optimization of the spatially variant PSF and the deconvolved image can be performed. In the ideal case of perfect information, it is shown that the algorithm is able to perfectly cancel the adverse effects of anisoplanatism down to the level of numerical precision. Exploring two different modes of deconvolution (using object bases of pixel values or stellar field parameters), we then quantify the performance of the algorithm in the presence of Poissonian noise for crowded and noncrowded stellar fields.

MISTRAL: a myopic edge-preserving image restoration method, with application to astronomical adaptive-optics-corrected long-exposure images

Deconvolution is a necessary tool for the exploitation of a number of imaging instruments. We describe a deconvolution method developed in a Bayesian framework in the context of imaging through turbulence with adaptive optics. This method uses a noise model that accounts for both photonic and detector noises. It additionally contains a regularization term that is appropriate for objects that are a mix of sharp edges and smooth areas. Finally, it reckons with an imperfect knowledge of the point-spread function (PSF) by estimating the PSF jointly with the object under soft constraints rather than blindly (i.e., without constraints). These constraints are designed to embody our knowledge of the PSF. The implementation of this method is called MISTRAL. It is validated by simulations, and its effectiveness is illustrated by deconvolution results on experimental data taken on various adaptive optics systems and telescopes. Some of these deconvolutions have already been used to derive published astrophysical interpretations.